Recently it has been found, by experimental work [Surface Science 605 (2011) 2073], that the ground state of the In-rich InAs (001) surface, is described by the Kumpf et al. structural model [Phys. Rev. Lett. 86 (2001) 3586], with top In atomic rows adjusted to account for coexisting different local structures. As the surface system is now well understood we use it for testing density functional theory (DFT) with Perdew–Burke–Ernzerhof functional, in the context of solving complex surface structures. Starting from different initial atomic configurations we relax the surface multiple times. It is found that it converges to a few different metastable structures. Scanning tunneling microscopy (STM) images of these structures are numerically simulated, using their DFT density of states and the Tersoff–Hamman approximation. By comparison to available experimental STM images it is found that some theoretical images do have their experimental counterparts while the lowest energy theoretical structures do not correspond to any experimental features. We analyze these results and we find that, for large surface unit cells, there is no sufficient accuracy in calculated total energy to conclude about the surface ground state. Nevertheless, it is shown that the DFT methods still yield the results useful in specific cases. Careful comparison of simulated STM patterns with experimental results is indispensable in order to screen out probable artifacts.